Holomorphic functions on a Banach space
نویسندگان
چکیده
منابع مشابه
Holomorphic functions on Banach spaces
This is a survey about some problems from the theory of holomorphic functions on Banach spaces which have attracted the attention of many researchers during the last thirty years.
متن کامل2 Quantum Normal Families : Normal Families of Holomorphic Functions and Mappings on a Banach Space
The authors lay the foundations for the study of normal families of holomorphic functions and mappings on an infinitedimensional normed linear space. Characterizations of normal families, in terms of value distribution, spherical derivatives, and other geometric properties are derived. Montel-type theorems are established. A number of different topologies on spaces of holomorphic mappings are c...
متن کاملBoundaries for Algebras of Holomorphic Functions on Banach Spaces
We study the relations between boundaries for algebras of holomorphic functions on Banach spaces and complex convexity of their balls. In addition, we show that the Shilov boundary for algebras of holomorphic functions on an order continuous sequence space X is the unit sphere SX if X is locally c-convex. In particular, it is shown that the unit sphere of the OrliczLorentz sequence space λφ,w i...
متن کاملNorm and Numerical Peak Holomorphic Functions on Banach Spaces
We introduce the notion of numerical (strong) peak function and investigate the denseness of the norm and numerical peak functions on complex Banach spaces. Let Ab(BX : X) be the Banach space of all bounded continuous functions f on the unit ball BX of a Banach space X and their restrictions f |B◦ X to the open unit ball are holomorphic. In finite dimensional spaces, we show that the intersecti...
متن کاملHolomorphic Functions on Strict Inductive Limjis of Banach Spaces
In this article we show that a number of apparently different properties coincide on tite set of holomorpitic functions on a strict inductive limit (aH inductive limits are asgumed to be countable and proper) of Banach spaces and that they are ¿II satisfied only ‘u tite trivial case of a strict inductive limit of finite dimensional spaces. Thus tite linear properties of a strict inductive Iimit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1970
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1970-12595-2